Introduction to Engineering Principles and Units

and Dimensions Energy and Heat Units Conservation of Energy and Heat Balances Introduction and Mechanisms of Heat Transfer

UNIT & DIMENSION

Dimensions

are: properties that can be measured such as length, time, mass, temperature properties that can be calculated by multiplying or dividing other dimensions, such as velocity (length/time)

Units

are means of expressing the dimensions such as feet or meter for length, hours/seconds for time.valid equation must be dimensionally homogeneous: that is, all additive terms on both sides of the equation must have the same unit

Every

CONVERSION OF UNITA

measured quantity can be expressed in terms of any units having the appropriate dimension convert a quantity expressed in terms of one unit to equivalent in terms of another unit, multiply the given quantity by the conversion factor factor a ratio of equivalent values of a quantity expressed in different units

To

Conversion

SYSTEM OF UNITS

a) SI system b) American engineering system c) CGS system

SYSTEM OF UNITSComponents of a system of units: Base units - units for the dimensions of mass, length, time, temperature, electrical current, and light intensity. Multiple units- multiple or fractions of base unit e.g. time can be hours, millisecond, year, etc. Derived units - units that are obtained in one or two ways: by multiplying and dividing base units; also referred to as compound units e.g. ft/min (velocity), cm2(area), kg.m/s2 (force)

FORCE AND WEIGHT

of an object is force exerted on the object by gravitational attraction of the earth i.e. force of gravity, g. of gravitational acceleration: g = 9.8066 m/s2 = 980.66 cm/s2 = 32.174 ft/s

Value

TRY THIS An

engineer who is working on the heat transfer analysis of a brick building in English units needs the thermal conductivity of brick. But the only value he can find from his handbooks is 0.72 W/m.oC, which is in SI units. To make matters worse, the engineer does not have a direct conversion factor between the two unit systems for thermal conductivity. Can you help him out? From your conversion table, you find that 1 W = 3.41214 Btu/h 1 m = 3.2808 ft 1oC = 1.8oF

HEAT & ENERGY

Heat

form of energy that is transferred across the boundary of a system at a given temperature to another system at lower temperature. Heat the energy required to raise the temperature of a substance by one degree.

heat required to change the temperature of a substance the heat given to a body, when the body is in such a state that the heat gained by it doesn't convert to latent heat, or the energy supplied is not used up to change the state of the system In thermodynamics, they are called thermal energy. Thermal

conductivities the property of a material that

indicates its ability to conduct heat.

PRINCIPLES OF HEAT TRANSFER

Heat

transfer is thermal energy transport due to a temperature difference. Thermal energy is associated with the translation, rotation, vibration and electronic states of the atoms and molecules that comprise the materials. It represents the cumulative effect of microscopic activities and is directly linked to the temperature of matter. Heat transfer occur because of a temperature difference driving force and heat flows from the high to the low temperature region. 3 mechanism of heat transfer are; i) Conduction ii) Convection iii) Radiation

BALANCE FOR HEAT TRANSFER

The general balance for heat transfer: (Rate of heat in) + (Rate of generation of heat) = (Rate of heat out) + (Rate of accumulation of heat)

If we assume steady-state heat transfer, no heat generation. rate of accumulation is zero. rate of heat input = rate of heat output. rate of heat transfer is then constant with time. temperature at various points in the system do not change with time. rate of a transfer process is equal to driving force over resistance Rate of = Driving Force

Transfer

Resistance (R)

Conduction: the transfer of heat from a solid to another solid touching each other. Convection: the transfer of heat by circulation or movement through liquid or gases. Radiation: the transfer of heat from an object traveling through a space until absorbed by another object.

CONDUCTION In

conduction, heat is transfer between the adjacent molecules because of the difference in their thermal energy. The hotter molecules have a greater energy and they give or impart an energy to the adjacent molecules which have lower energy levels. e.g.: when we heat one side of a metal plate, the other side will also become hot. This is because heat is transfer in that metal plate by conduction. Energy can also be transferred by free electrons, which is quite important in metallic solids.

CONDUCTION: FOURIERS LAW

Flux of conduction heat transfer can be calculated by Fouriers Law qx dT k Fouriers Law A dx qx : heat-transfer rate in the x direction (SI: W or J/s; cgs: cal/s; Eng.: btu/h) A : cross sectional are normal to the heat flow (m2) k : thermal conductivity ( SI: W/m. K; cgs: cal/s. cm. C; Eng.: btu/h. F. ft ) dT/dx : temperature different in the x direction The minus sign is required in Fouriers equation because the heat transfer is positive in the direction from initial point 1 to the final point 2. Since the T1 > T2 (heat is transport from high temperature to lower temperature region), minus sign is needed to make the value of heat rate positive.

EXERCISE 1 One

face of a copper plate 3 cm thick is maintained at 400oC, and the other face is maintained at 100oC. How much heat is transferred through the plate per unit area if k(copper) = 370 W/m.oC?

Answer:

3.7 MW/m2

CONVECTION: NEWTONS COOLING EQUATION

Convection transfer of heat by bulk transport and mixing of macroscopic element of warmer portions with cooler portions of a gas or a liquid. It often involves the energy exchange between a solid surface and a fluid. Example : loss of heat from radiator where air is circulated by a fan. q hA(Tw T f )

2 types of convection: Natural Convection - motion of the fluid arises solely due to the temperature differences existing within the fluid. Example: hot air rising off the surface of a radiator. Forced Convection - motion of the fluid is imposed externally (such as by a pump or fan). Example: a fan-powered heater, where a fan blows cool air past a heating element, heating the air.

CONVECTION HEAT TRANSFER

TwFluid Flowing

Tf q

q hA Tw T f

Tf 1 hA

Tf R

EXERCISE 2 Air

at 20oC blows over a hot plate 50 by 75 cm maintained at 250oC. The convection heat transfer coefficient is 25 W/m2.oC. Calculate the heat transfer.

Answer:

2.156 kW

RADIATION HEAT TRANSFER

Radiation is the transfer of energy through a space by electromagnetic waves. One of the easiest example is the transfer of heat from the sun to the earth. When thermal radiation falls upon a body, a part of this radiation is absorbed as heat, a part is reflected back into space and a part may be transmitted into body. Radiation heat transfer can be calculate from Stefan-Boltzmann equation: 4 4 q A1 (T1 T2 )